= ∑ n1>...>nr>0 q11 . . . qirnrn1 1 . . . n −sr r , with q a root of unit and i = (i1, . . . , ir) a composition. These sums converge when s1 > 1. To study simultaneously these families of polyzêtas, the colored Hurwitz polyzêtas, for a composition s = (s1, . . . , sr) and a tuple of complex numbers ξ = (ξ1, . . . , ξr) and a tuple of parameters in ]−∞; 1[, t = (t1, . . . , tr), are defined by [6]

We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the G-module structure of the push-forward to the base of any sheaf on a family of admissible G-covers. This formula can be interpreted as a representation-ringvalued relative Riemann-Hurwitz formula for fam...

We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding “extremal” Hurwitz p...

Let D2N be the dihedral group of order 2N , Dic4M the dicyclic group of order 4M , SD2m the semidihedral group of order 2 m, and M2m the group of order 2 m with presentation M2m = 〈α, β | α 2m−1 = β2 = 1, βαβ−1 = α2 m−2+1〉. We classify the orbits in Dn 2N , Dic n 4M , SD n 2m , and M n 2m under the Hurwitz action.

In defining a special type of group, such as commutative group or finite group, one may be content to add a suitable postulate, or possibly a number of postulates, describing the special property under consideration, to any set of postulates for a general group. I t is, however, of interest to pursue the matter further, to determine whether a simplified set of postulates can be set up which wil...

f(x1, . . . , xd) ∈ Ud (C) ⇐⇒ f(ıx1, . . . , ıxd) ∈ Hd(C) Consequently, many of the properties of H(C) follow immediately from the properties of U (C), and their proofs will be omitted. See [1–7, 13] for more information about U (C) and H(C). We use the notation in [7], and let RHP denote the right half plane. We do not cover well-known topics in one variable such as Routh-Hurwitz, the Edge the...

Hurwitz groups are the nontrivial finite quotients 2 3 7 of the ( 2 , 3 , 7 ) triangle group (x, y\x — y = (xy) = 1) . This paper gives a brief survey of such groups, their significance, and some of their properties, together with a description of all examples known to the author.

In this work, we investigate the dynamical behavior of a fractional order cholera model. All the feasible equilibria for the system are obtained and the conditions for the existence of interior equilibrium are determined. Local stability analysis of the cholera model is studied by using the fractional Routh-Hurwitz stability conditions. Our results indicate the potential of fractional-order cho...

We provide an explicit formula for the Tornheim double series T (a, 0, c) in terms of an integral involving the Hurwitz zeta function. For integer values of the parameters, a = m, c = n, we show that in the most interesting case of even weight N := m + n the Tornheim sum T (m, 0, n) can be expressed in terms of zeta values and the family of integrals